Karzai's visit to Washington has coincided with widespread anger in Afghanistan over the reported deaths of dozens of civilians in an alleged US raid on Monday in the western province of Farah.
Asked about the Farah deaths, Karzai said all US politicians had expressed regret and "emphasised the need for working out measures that will reduce and eliminate eventually the possibility of civilian casualties".
"It causes pain to Afghans, it is something we want to have addressed very, very seriously and in a manner that will soon end casualties to the Afghan people," he said.
John Kerry, the Chairman of the Senate Foreign Relations Committee, praised the two leaders for answering US politician's questions about the conflict, now in its seventh year in Afghanistan.
"All of the Senators who were present today were encouraged by the reality with which both presidents addressed the questions and summarized the challenge," Kerry told reporters.
Karzai, who is to run for re-election in August, said the talks "brought us to the right light of mind on questions that we have together" and again pledged closer cooperation.
Zardari said meeting senators who play a key role in overseeing US aid to Pakistan and Afghanistan "brings strength to the situation that we have and anything that brings strength is very good".
Al Jazeera's James Bays in Washington said the meetings between Afghan and Pakistani leaders appeared to have gone well but that no specific policy pledges had been made.
Barack Obama, the US president, promised on Wednesday a "lasting commitment" to Afghanistan and Pakistan after holding talks with the two nations' leaders in Washington DC.
He said the two countries, along with the US, shared a common goal of dismantling, disrupting and defeating al-Qaeda, the Taliban and its allies, and improving security in the neighbouring nations.
"Our strategy reflects a fundamental truth, the future of Afghanistan, Pakistan and the US are linked," Obama said.
Obama praised both Karzai and Zardari as fully appreciating the "seriousness" of the situation in the region.
However, he cautioned that people should expect more violence and more setbacks.
Obama has pledged to deal with the situation in the two countries with a joint strategy that deploys about 20,000 more troops to Afghanistan to combat the rising threat from Taliban and al-Qaeda fighters and hand billions of dollars in aid to Pakistan.